# Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

- Volume: 35, Issue: 1, page 165-189
- ISSN: 0764-583X

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topBostan, Mihai. "Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.1 (2001): 165-189. <http://eudml.org/doc/194041>.

@article{Bostan2001,

abstract = {The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.},

author = {Bostan, Mihai},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {electro-magnetism; Maxwell equations; Vlasov equation; finite volumes},

language = {eng},

number = {1},

pages = {165-189},

publisher = {EDP-Sciences},

title = {Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems},

url = {http://eudml.org/doc/194041},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Bostan, Mihai

TI - Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 1

SP - 165

EP - 189

AB - The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

LA - eng

KW - electro-magnetism; Maxwell equations; Vlasov equation; finite volumes

UR - http://eudml.org/doc/194041

ER -

## References

top- [1] A. Arsenev, Global existence of a weak solution of Vlasov’s system of equations. USSR Comp. Math. Math. Phys. 15 (1975) 131–143.
- [2] K. Asano and S. Ukai, On the Vlasov-Poisson limit of the Vlasov-Maxwell equation. Pattern and waves. Qualitative analysis of nonlinear differential equations. Stud. Math. Appl. 18 (1986) 369–383. Zbl0623.35059
- [3] N. Ben.Abdallah, Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system,. Math. Meth. Appl. Sci. 17 (1994) 451–476. Zbl0806.35172
- [4] M. Bezard, Boundary value problems for the Vlasov-Maxwell system, in Semin. Équ. Deriv. Partielles, Ec. Polytech., Cent. Math., Palaiseau Semi 1992–1993, Exp. No. 4 (1993) 17. Zbl0878.35107
- [5] B. Bodin, Modélisation et simulation numérique du régime de Child-Langmuir. Thèse de l’École Polytechnique, Palaiseau (1995).
- [6] M. Bostan and F. Poupaud, Periodic solutions of the Vlasov-Poisson system with boundary conditions. C. R. Acad. Sci. Paris, Sér. I 325 (1997) 1333–1336. Zbl0895.35079
- [7] M. Bostan and F. Poupaud, Periodic solutions of the Vlasov-Poisson system with boundary conditions. Math. Mod. Meth. Appl. Sci. 10 (1998) 651–672. Zbl1019.76047
- [8] M. Bostan and F. Poupaud, Periodic solutions of the 1D Vlasov-Maxwell system with boundary conditions. Math. Meth. Appl. Sci. 23 (2000) 1195–1221. Zbl0965.35010
- [9] M.O. Bristeau, R. Glowinski and J. Périaux, Controllability methods for the computation of time periodic solutions; application to scattering. J. Comp. Phys. 147 (1998) 265–292. Zbl0926.65054
- [10] J.P. Cioni, Résolution numérique des équations de Maxwell instationnaires par une méthode de volumes finis. Ph.D., Université de Nice Sophia-Antipolis (1995).
- [11] J.P. Cioni, L. Fezoui and D. Issautier, High-order upwind schemes for solving time-domain Maxwell equation. La Recherche Aérospatiale No. 5 (1994) 319–328.
- [12] P. Degond, Regularité de la solution des équations cinétiques en physiques de plasmas, in Semin. Équ. Dériv. Partielles 1985–1986, Exp. No. 18 (1986) 11. Zbl0613.35070
- [13] P. Degond, Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity. Math. Methods Appl. Sci. 8 (1986) 533–558. Zbl0619.35088
- [14] P. Degond, Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in 1 and 2 space dimensions. Ann. Sci. Ec. Norm. Super. IV. Ser. 19 (1986) 519–542. Zbl0619.35087
- [15] R.J. Diperna and P.L. Lions, Global weak solutions of Vlasov-Maxwell system. Comm. Pure Appl. Math. XVII (1989) 729–757. Zbl0698.35128
- [16] C. Greengard and P.A. Raviart, A boundary value problem for the stationary Vlasov-Poisson system. Comm. Pure Appl. Math. XLIII (1990) 473–507. Zbl0721.35084
- [17] Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions. Comm. Math. Phys. 154 (1993) 245–263. Zbl0787.35072
- [18] Y. Guo, Regularity for the Vlasov equation in a half space. Indiana Univ. Math. J. 43 (1994) 255–320. Zbl0799.35031
- [19] P.L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105 (1991) 415–430. Zbl0741.35061
- [20] R. Löhner and J. Ambrosiano, A finite element solver for the Maxwell equations, in GAMNI-SMAI conference on numerical methods for the solution of Maxwell equations, Paris (1989).
- [21] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in 3 dimensions for general initial data. J. Diff. Eq. 95 (1992) 281–303. Zbl0810.35089
- [22] F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system. Forum Math. 4 (1992) 499–527. Zbl0785.35020

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